Method and apparatus for low signal to noise ratio instantaneous phase measurement

ABSTRACT

The system and method of the present invention generates high resolution phase measurements without the high processing and memory overhead requirements found in prior art circuits and methods. Each signal sample (of N samples) is divided further into J segments each segment having K samples. The frequency is computed with respect to one J segment and is used in the phase measurement computations performed for the remaining segments. The phase measurements performed with respect to each J segment are then averaged to compute a high resolution phase measurement for the corresponding N segment.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to the phase measurements. Moreparticularly, the present invention relates to cost effective real timephase measurements in a low signal to noise ratio environment.

2. Art Background

In numerous communication, instrumentation and measurement applications,an instantaneous phase measurement is required. However, noisy signals(of Signal to Noise Ratio (SNR) less than 0 dB) are occasionallyencountered. Moreover, for most of these applications, the frequency ofthe incoming signal is unknown and needs to be measured prior tocomputing the phase measurement. This follows from the fact that phasemeasurement algorithms require that the signal frequency be resolved tobetter than ##EQU1## where T_(obs) is the observation time. Thissignificantly complicates the phase measurement task. Zero crossingtechniques, such as counters, and Phase Lock Loops (PLL) have beenwidely used for both frequency and phase measurements. Using the countermethod, the phase between two signals is measured by measuring thesignal period and comparing it with the time between the positive slopezero crossing of the two signals. In the PLL method, a VoltageControlled Oscillator (VCO) is used to generate a reference signal withfrequency equal to the input signal. The phase of the signal is thenmeasured with respect to the input signal using analog or digitalmultipliers (AND gate) followed by averaging circuit. Unfortunately,both methods fail to work with SNR lower than 10 dB. Phase measurementscan also be achieved using the Fourier analysis method. The frequency isfirst estimated by computing the signal spectrum and extracting thefrequency at the point the signal has its maximum power. A referencesinusoidal signal is then generated. The frequency of the referencesignal with respect to the reference signal is then computed bysubtracting the two measurements of phase.

Using the Fourier analysis method, phase measurement accuracy isinversely proportional to the time of measurement (i.e., the time overwhich the signal is observed and processed) and the SNR. When sampleddata is used, the variance of the phase is then given by: ##EQU2## whereΦ represents the phase SNR represents the signal to noise ratio and Nrepresents the number of samples.

For a specified SNR, the only way to improve the phase measurementaccuracy is by increasing the number of samples N. If the signalfrequency is known, then the complexity of the phase measurementalgorithm will be given by ν(N) (i.e., the number of the computations νis proportional to the number of samples). The significant increase inthe algorithm complexity occurs when the frequency is unknown and it hasto be estimated with an accuracy better than ƒ_(s) /N, where ƒ_(s) isthe sampling frequency. The FFT algorithm is one of the most efficientalgorithms for this task and its complexity is given by ν*(N log N).Thus, the complexity of frequency measurement algorithm is an order ofmagnitude greater than the complexity of the actual phase measurementalgorithm. Moreover, for frequency measurement, a temporary buffer of Ncells has to be allocated to store all the samples required forfrequency measurement. Additional control circuitry is also needed torecall these samples for phase measurement. It should be noted that ifthe frequency is known, only a multiplier and an accumulator are neededto perform the task of phase measurement. In summary, the need tomeasure the frequency significantly increases the processing and memoryrequirements. The processing and memory requirements for the actualphase measurement involve only a small fraction of what is required forfrequency measurement.

SUMMARY OF THE INVENTION

The system and method of the present invention generates high resolutionphase measurements without the high processing and memory overheadrequirements found in prior art circuits and methods. Each signal sample(of N samples) is divided further into J segments each segment having Ksamples. The frequency is computed with respect to one J segment and isused in the phase measurement computations performed for the remainingsegments. The phase measurements performed with respect to each Jsegment are then combined to compute a high resolution phase measurementfor the corresponding N segment.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects, features and advantages of the system and method of thepresent invention will be apparent to one skilled in the art from thefollowing detailed description in which:

FIG. 1 is a simplified flow diagram of one embodiment of the method ofthe present invention.

FIG. 2 is a simplified block diagram of one embodiment of the circuit ofthe present invention.

FIG. 3 is a simplified block diagram of one embodiment of a phasemeasurement circuit utilized to calculate the phase of each segment inaccordance with the teachings of the present invention.

FIG. 4 is a simplified block diagram of a circuit for combining thephase measurements of the individual J segments to determine the finalphase measurement value.

FIG. 5 is a simplified block diagram of an alternate embodiment of aphase measurement circuit utilized to calculate the phase of eachsegment in accordance with the teachings of the present invention.

FIGS. 6a and 6b illustrate that increasing quantization levels beyond 1bit quantization when operating in a large amplitude signal dynamicrange does not result in significant improvement.

FIG. 7 is a block diagram illustration of circuitry to overcomeambiguity in phase measurement in accordance with the teachings of thepresent invention.

DETAILED DESCRIPTION

In the following description, for purposes of explanation, numerousdetails are set forth, in order to provide a thorough understanding ofthe present invention. However, it will be apparent to one skilled inthe art that these specific details are not required in order topractice the present invention. In other instances, well knownelectrical structures and circuits are shown in block diagram form inorder not to obscure the present invention unnecessarily.

A simplified flow diagram of the method performed to determine phasemeasurements in accordance with the teachings of the present inventionis set forth in FIG. 1. At steps 105, 110, the signal sampled data of Nsamples is divided into J (to be determined) segments. Each segmentcomprises K samples. The number of K is chosen based on the SNR of thesignal. After choosing K, J can be determined as: J=N/K (N is the totalnumber of samples used for phase measurement, K is the number of samplesfor each segment).

For simplicity in implementation, it is preferred that K is chosen to beas small as possible. For example, phase measurements can be performedusing a K value of 3 (i.e., using only three samples). Hardwaresimplicity is achieved as in such an embodiment, a correspondinghardware implementation would require only one look-up table and oneaccumulator. However, as the signal to noise ratio (SNR) gets lower, therms in the phase measurement becomes larger and may cause the phasemeasurement to deviate more than π from its actual value. This causes awrap around in the measurement result. In such as situation, the phasemeasurement is ambiguous and a large number of samples (K) should beused. Therefore, for low SNR applications, the number of samples shouldbe chosen large enough to avoid ambiguities. Thus preferably, K isselected such that the rms in phase measurement at the minimum expectedSNR is much less than π to avoid phase measurement ambiguity.

Once K is selected, J is then computed as J=N/K. Where N is the totalnumber of samples used to perform phase measurement of the signal, K isthe number of samples of each segment and is determined by the signalSNR and J is the number of segments.

As discussed above, the values of J and K are determined based upon thesignal to noise ratio (SNR) of the signal. The values can be determineda variety of ways. For example, the SNR and values of K and J can bedetermined empirically to generate values of K and J that are programmedinto the process or circuit. Alternatively, it is contemplated that thevalues of J and K can be determined by sampling the signal prior toinitiating the process described herein and the circuit parameters setwith the values of J and K determined. For example, the SNR can bemeasured using circuitry and methods well known to those skilled in theart and the values of K and J determined from the measured value.Alternatively, the process includes the steps of determining K and J.Likewise, the corresponding circuitry therefore includes logic todetermine the values of K and J. The output of the circuitry is coupledto control the frequency measurement circuitry and phase measurementcircuitry discussed below in order to provide the parameters K and J.

At step 115, the frequency is measured for the first segment.Preferably, the signal frequency is measured with an accuracy betterthan f_(s) /K, where f_(s) is the sampling frequency. More particularly,the level accuracy can be determined considering the following:

Consider the signal: s(t)=r(t)+jq(t) where r(t)=A cos(2πƒ₁ t+φ)+n(t),q(t)=A sin(2πƒ₁ t+φ)+n^(v) (t), where ƒ₁ represents the signal frequencyand φ represents the phase of the signal, n^(v) (t) is the Hilberttransform of n(t). Let ƒ₂ be the frequency estimated and used for phaseestimation. Using the Fourier analysis method to compute the phase ofthe s(t), the signal phase is given by: ##EQU3## where T is the timeover which the phase is measured.

With n(t)=0 (i.e., clean signals), the estimated phase (φ_(es)) of thesignal is given by:

    φ.sub.es =φ+λ

where φ is the phase of the signal and ##EQU4## and Δƒ=ƒ₁ -ƒ₂ (i.e., thedifference between the actual signal frequency and frequency used forphase measurement). To accurately measure the phase of the signal, λshould be much smaller than 1. To ensure that (λ<<1), ΔƒT should be muchsmaller than one. This can be achieved if the frequency used for phasemeasurement is estimated with high precision. This typically requires ahighly complicated hardware if the absolute value of the signal phase isrequired. Fortunately, hardware can be simplified for phase differencemeasurement. In particular, the phase difference between two signals s₁(t) and s₂ (t) is given by:

    (φ.sub.d).sub.es =φ.sub.es1 +λ-φ.sub.es2 -λ=φ.sub.d =actual phase difference.

Therefore, for the measurement of the phase difference between two cleansignals, there is no need to estimate the signal frequency. However,when noise is added to the signals, the estimated phase value is:##EQU5## where, ##EQU6## To optimize the phase measurement, μ and υshould be made as small as possible. The numerators of υ and μ arecharacteristics of the signal and the noise and cannot be controlled.However, the numerator is a function of Δƒ (i.e., how accurate thefrequency is measured). Thus, μ and υ can be minimized by maximizing thedenominator. This can be achieved by keeping the denominator Ψ close toits maximum value of one where, ##EQU7## For TΔƒ≦2, Ψ is greater than orequal to 0.65 and for TΔƒ≦4, Ψ is greater than or equal to 0.9. Thiscorresponds to only a minimal loss in SNR of 1.5 and 0.4 dB,respectively. The above equations indicate that precise frequencymeasurement is not necessary to attain a value close to one for Ψ. Avalue of ΔƒT=4 means that the frequency needs to be measured withaccuracy four times better than that obtained with the DTF method. Thistask is feasible an can be implemented in real time.

Several well known methods, such as zero crossing counting and the fastFourier Transform (FFT) algorithm, can be used for frequency measurementwith an accuracy similar or better than what is required by the abovederivation. For low SNR (less than 10 dB), only the FFT algorithmprovides reliable measurements. For example, the structure and methoddescribed in copending U.S. patent application Ser. No. 07/942,044 forMethod and Apparatus for Improvised Digital Signal Processing usingDiscrete Fourier Transform, filed Sep. 8, 1992 is used. Moreparticularly, the method for determining the frequency consists of thefollowing steps: dividing the signal into a plurality of concurrentsignals, converting each of the plurality of concurrent signals into anencoded signal by performing an analog to digital conversion, thesampling of each of the concurrent signals being done at a differentsampling frequency, performing a discrete Fourier transform (DFT) oneach of the encoded signals by utilizing the encoded signals to access adecoding or memory storage device, the individual memory locations ofthat device having stored therein the value of the DFT corresponding tothe binary representation of the address of the memory location, andcombining the results of the individual DFTs to determine the frequency(for example, according to a radix-r representation of number). Thismethod offers significant reduction in the number of computations overprior art the FFT method. Using this method with the method of thecurrent invention for computing phase measurements described herein, arelatively simple real time Fourier analysis based processor can beimplemented for both frequency and phase measurements.

Once the frequency is determined for one J segment, the same frequencyvalue is applied to computation of the phase measurement for eachsegment. At step 120, the phase measurement for each segment iscomputed. The phase measurement φ_(i) is determined according to thefollowing:

If q_(i) =1 then φ_(i) =θ

If q_(i) =2 then φ_(i) =π-θ

If q_(i) =3 then φ_(i) =π+θ

If q_(i) =4 then φ_(i) =2π-θ

where q_(i) represents the quadrant of the phase measurement, and θ isdetermined according to the following: ##EQU8## where k_(s) is theestimated signal frequency normalized to the sampling frequency and0≦θ<π/2.

At step 125, the phase measurement values determined for each J segmentare then combined to achieve the final phase measurement value φ.Combining the phase measurement values is not a straightforward taskbecause of the wrap around 2π of the phase values. The following methodis devised for real time calculation of the final phase measurementvalue. The phase measurement values are summed to form the valueΦ_(ACC). The number of phase measurements that fall into each quadrantis also determined. The final phase measurement value φ is determined tobe: ##EQU9## J_(VAL) represents the number of valid segments and q 4!represents the number of valid phase measurements in the fourthquadrant.

If the quadrants in which the phase measurements fall in more than twoadjacent quadrants then the current phase measurement can be rejected.This can be used as an additional criterion to validate the phasemeasurement. This follows from that if phase measurements fall into morethan two quadrants, then the measured phase varies by more than π/2 andthese measurements should be rejected for accurate phase measurementresults.

In the following, the computational reduction offered by this method isestimated. As said earlier, only the frequency of the one segment iscomputed and the number of computations is therefore minimized. Inparticular, the number of computations required for frequencymeasurement is given by K log K and the reduction in computation isgiven by: ##EQU10##

For example, if N=1024 and K=64, then the sampled data is divided into16 segments and the number of computations using the present inventionis reduced by a factor of thirty. This reduction in computation issignificant when real time processing is considered. Furthermore, forthis example, the memory required is only one sixteenth of that requiredwith the available methods. In addition, almost the same accuracyattained by the optimum scheme can be achieved with the presentinvention. To illustrate the above and using K samples, the number ofsegments can be calculated from the equation J=N/K. By combining J phasemeasurements and assuming that these measurements are independent, thephase variance is given by: ##EQU11## For N>>J, the accuracy is almostthe same as that provided by the Cramer-Rao Bound and is given by:##EQU12##

FIG. 2 illustrates one embodiment of the circuit of the presentinvention. In the present embodiment, the in-phase r(t) and quadratureq(t) signals are sampled by samplers 230, 235 at sampling frequencyf_(s) and digitized to result in sample data r(i) and q(i). The sampleddata r(i) and q(i) is processed through a K sample delay line 220, 225to offset the time delay required to measure the frequency. The delayedsignals are then applied to the frequency measurement unit 210 and phasemeasurement unit 205. Preferably the sampled data is also input to burstdetector 215. The burst detector is used in applications where burstsignals are encountered. For these applications, the burst detector isused to estimate the burst length. Once the burst detector detects thepresence of the signal, both the frequency and phase measurement units(210 and 205) are enabled. The phase measurement unit keeps on combiningthe phase measurements of the different signal segments until the burstdetector detects the end of the signal. This ensures that the entiresignal is processed for phase measurement and optimum measurement isattained. When the signal is continuous, the bust detector is optional.However, it can also be utilized to reject segments of the signal wherethe SNR is lower than a certain threshold.

The frequency measurement unit 210 computes the frequency for a singlesegment and is input to the phase measurement unit 205 for computationof the phase measurement values for each segment and the final outputphase value.

FIG. 3 is a block diagram of one embodiment of the portion of the phasemeasurement unit (205 FIG. 2) which is used to calculate the phase ofeach segment according to the following:

If q_(i) =1 then φ_(i) =θ

If q_(i) =2 then φ_(i) =π-θ

If q_(i) =3 then φ_(i) =π+θ

If q_(i) =4 then φ_(i) =2π-θ

where ##EQU13## which corresponds to: tan⁻¹ (x/y) In particular,multipliers 305, 310, 315, 320, adders, 325, 330 and accumulators ACCX335 and ACCY 340 are used to compute the x and y values which are inputto logic 345 for computation of tan⁻¹ (x/y) and q_(i). The phase θ=tan⁻¹x/y can be measured using high speed ROMs. q_(i) is computed based onthe sign of the quantities x and y and as follows:

q_(i) =1 if x,y≧0

q_(i) =2 if x≧0,y<0

q_(i) =3 if x<0,y≧0

q_(i) =4 if x,y<0

The circuit also computes the signal power which is used to determinethe validity of the current measurement (generates validation bit). Thesignal power is computed by adding the square of the outputs of the twoaccumulators 335, 340. This can be achieved using high speed ROM (350).The output of the ROM 350 is then used as an estimate of the signalpower at the estimated signal frequency. If the power is less than apredetermined threshold, the current phase measurement is rejected. Thethreshold is set to an acceptable minimum detectable signal power.

FIG. 4 is a simplified block diagram of one embodiment of a circuit forcalculating the final phase measurement value. Each phase measurementvalue for each segment φ_(i) is input to accumulator 405. Anidentification of the corresponding quadrant in which the phasemeasurement value occurs is input to accumulator 410 which maintains acount of the number of phase measurement values occurring in eachquadrant.

Control logic 415 receives as input the output of the burst detector,the validation bit and the sampling frequency used to determine thefrequency value used in the phase measurement calculates. The output ofthe control logic is used to enable the accumulators 405 and 410whenever the burst detector is on and the validation bit indicates thepresence of a valid phase measurement.

The accumulated phase measurement value and the quadrant counts ofoccurrences of the phase measurement value are input to logic 420 whichgenerates the final phase measurement value, preferably determinedaccording to the following: ##EQU14##

FIGS. 2-4 illustrate one embodiment of the circuit of the presentinvention. However, applications where the sampling frequency (f_(s)) is40 MHz or higher, multiplier-accumulators with execution time of 25 nsor less are required. These components are expensive and typically areused only for special purpose signal processing applications. In analternate embodiment, to minimize cost, several multiplier-accumulatorsreplace single multipliers or accumulators used and the processing isperformed in parallel. The hardware complexity of this scheme isdetermined by the number of the multiplier-accumulators used. The numbertypically is equal to or higher than the multiplication of the samplingfrequency by the multiplication-accumulation execution time.

As the sampling frequency increases, so does the number of multipliersand accumulators. At sampling frequencies higher than 120 MHz, thehardware implementation is rather intricate. For these applications, itis preferred to use an alternate embodiment illustrated by FIG. 5. FIG.5 is a simplified schematic diagram of an embodiment which uses highspeed look-up tables (LUTs) (such as high speed ROMs or RAMs). Temporarybuffers 505, 510 are used to store N_(s) a certain number of samples.This number of samples stored is chosen to be equal to or greater thanthe product of multiplication of the sampling frequency (f_(s)) and thelook-up table access time. Each time the buffer is full, its content islatched by latches 515, 520 and used as an input to the lookup tables525, 530. The other two inputs for the look-up tables 530, 525 are thefrequency and the phase of the reference signal. Look-up tables LUT1 525and LUT2 530 store precomputed values of the multiplication-accumulationof the several samples of the input signal with the correspondent valuesof the reference signals (i.e., cos(2πik_(s) /k) similar to those shownin FIG. 3). Since LUTs are used for this implementation, only theintegers (i/N_(s)) are used as input for the LUT to represent the phaseof the reference signals. Thus, with each look-up table cycle, severalmultiplication-accumulation operations are performed. Because of thelimitation in the number of the look-up table inputs, this approach issuitable when high speed (100 MHz and higher) low resolutionanalog-to-digital converters (ADCs) are used. The output of LUTs 525,530 are input to accumulators 535,540 which provide the input to logic545 for computation of φ_(i) and q_(i).

In the above discussion, it is assumed that the number of samples usedfor the frequency measurement and the phase measurement is the same.However, different numbers of samples can be used. It is essential thatthe frequency measurement be accurate for reliable phase measurement.Therefore, for the cases where low SNR is encountered, it may beadvantageous to use a larger number of samples for frequency measurementthan the number of samples used for phase measurement.

It is recognized that an ambiguity in phase measurement can occur whenthe sampling frequency f_(s) is exactly equal to multiple integer L ofthe signal frequency. At these frequencies, the effective number ofsamples used for the phase measurement are reduced from K to L. Thisfollows from the fact that the sampled data will repeat itself after Lsamples. Typically, the problem happens only with high SNR signals (20dB or higher). As more noise is added to the signal, the problem becomesless noticeable. One of the strategies that is currently used toalleviate the effect of this problem is by increasing the number ofsamples or the sampling frequency or both. In some applications, thesetechniques are not effective due to the limitations posed by the signaltransit time. The signal transit time is the time over which the signalis present and it is the same time over which the signal is observed andprocessed.

It should be noted that the above problem can be alleviated for thecases where the signal amplitude dynamic range in low by using highresolution ADCs. However, for the cases where a large amplitude signaldynamic range (>10) is encountered, increasing the number ofquantization levels does not provide significant improvement over 1-bitquantization. FIGS. 6a and 6b are used to illustrate this point. FIG. 6ashows a trajectory of the signal s(t)=i(t)+jq(t)=A(sin(2πt)+j cos(2πft))in the complex plane. For these figures, the signal dynamic range isassumed to be 1:1000 (e.g., the signal amplitude varies from 1 mV to1000 mV) and an 8-bit ADC be used for signal quantization. To quantizesmall signals with reasonable resolution, each quantization level shouldbe much smaller than 1 mV. If the quantization level is chosen to be0.25 mV, the maximum signal that can be sampled accurately with the8-bit ADC is 82 mV (or 8% of the input signal dynamic range). If thesignal s(t) is sampled at ƒ_(s) /4, then it can be easily shown that theambiguity in phase measurement can be as large as 90-2 sin⁻¹ 0.25=61°.This example demonstrates that using high resolution ADCs does not offersignificant improvement over the much simpler implementation using 1-bitADC. One may argue that this problem can be resolved by using a higherresolution (more than 8-bit) ADC. However, such ADCs are expensive andthey are not available to cover signal bandwidths over 20 MHz. Anotherargument is to spread the quantization levels in the previous example tocover the signal dynamic range more efficiently. While thissignificantly complicates the implementation, it does not providesignificant improvement. FIG. 6b shows a logarithmic scale for thequantization levels that is used to compress signals with highamplitudes and to stretch signals with low amplitudes. With thisconfiguration, it can be shown that the phase ambiguity at ƒ_(s) /4 canbe as large as 30°.

FIG. 7 illustrates an alternate embodiment for generating the real andcomplex sampled signals r(i) and q(i) that provides an elegant solutionto this problem. Logic control 705 receives as input the samplingfrequency f_(s) to be used and the output of the burst detector (forthose applications which process burst signals) and generates a controlsignal to decoder 710 to select the input signal to be output by decoder710 (i.e., f_(s), f_(s) (τ), f_(s) (2τ) . . . ) generated by inputsf_(s) 725 and delays 730, 735, 740. The output of decoder 710 is used tocontrol the timing of the samples of inputs r(t) and q(t) by ADCs 715,720 to generate sampled signals r(i) and q(i). Thus, instead of samplingthe different signal segments with the same sampling frequency, only thefirst segment is sampled using f_(s). For the second segment, f_(s) isshifted by τ and then used to sample the second segment. For the thirdsegment, f_(s) is delayed by 2 τ and so on. The time delay τ is chosensuch that f_(s) τ is a number that is not rational. This ensures thatthe sampling pattern of each segment is different from the rest. Withthis scheme, the rms error of the final phase measurement converges tothe actual phase rms error given by Cramer₋₋ Rao bound. It should benoted that many other schemes can be easily adapted to serve the samepurpose. For example, instead of using different time delayed versionsof the sampling frequency to provide different signal patterns,different sampling frequencies can be used to do the same function.Furthermore, for the applications where transit time is short for thecases where the number of samples in each segment is large, the samplingfrequency for each segment can be modulated. A simple implementation ofthis scheme is achieved by phase modulating the positive going edge ofthe sampling frequency while preserving its negative going edge. Thisensures phase modulating the sampling frequency without changing itsfrequency. This will overcome the ambiguity associated with each phasemeasurement.

The invention has been described in conjunction with the preferredembodiment. It is evident that numerous alternatives, modifications,variations and uses will be apparent to those skilled in the art inlight of the foregoing description.

What is claimed is:
 1. A method for measuring phase for N samples of asignal comprising the steps of:determining a number of K samples withinan N sample; identifying a number of J segments within an N sample, eachJ segment composed of K samples; computing a frequency measurement ofthe signal for one of the J segments; computing a phase measurement ofeach J segment using the frequency computed for one of the J segments;combining the phase measurement of each J segment to generate a combinedphase measurement indicative of the phase measurement of the N sample ofthe signal.
 2. The method as set forth in claim 1, wherein the step ofdetermining the number of K samples comprises the step of determining Kbased upon the signal to noise ratio (SNR) of the signal.
 3. The methodas set forth in claim 1, wherein the step of determining the number of Ksamples comprises the step of determining K such that rms in phasemeasurement at the minimum expected signal to noise ratio (SNR) of thesignal is less than π.
 4. The method as set forth in claim 1, whereinthe step of identifying the number of J segments comprises determining Jaccording to the following equation: J=N/K.
 5. The method as set forthin claim 1, wherein the step of computing the frequency comprises thesteps of:dividing the J segment of the signal into a plurality ofsampled signals, each sampled signal sampled at a different samplingfrequency:performing a discrete Fourier transform (DFT) on each sampledsignal; and combining the results of the DFT sampled signals todetermine the frequency.
 6. The method as set forth in claim 1, whereinthe step of computing the frequency comprises using zero crossingcounting.
 7. The method as set forth in claim 1, wherein the step ofcomputing the frequency comprises using a fast Fourier transform (FFT).8. The method as set forth in claim 1, wherein the step of computing aphase measurement for each J segment comprises determining the phasemeasurement according to the following:If q_(i) =1 then φ_(i) =θ Ifq_(i) =2 then φ_(i) =π-θ If q_(i) =3 then φ_(i) =π+θ If q_(i) =4 thenφ_(i) =2π-θwhere q_(i) represents the quadrant of the phase measurement,and θ is determined according to the following: ##EQU15## where k_(s) isthe estimated signal frequency normalized to the sampling frequency and0≦θ<π/2.
 9. The method as set forth in claim 1, wherein the step ofcombining the phase measurement of each J segment to generate a combinedphase measurement comprises the steps of:summing the phase measurementvalues of the J segments to generate a summed value Φ_(ACC) ;determining the number of phase measurements that fall into eachquadrant; and determining the combined phase measurement according tothe following; ##EQU16## where J_(VAL) represents the number of validphase measurements, q₁, q₂, . . . q_(JVAL) represent the quadrants ofvalid phase measurements, and q 4! represents the number of valid phasemeasurements that falls into the fourth quadrant.
 10. A method formeasuring phase for N samples of a signal comprising the stepsof:computing a frequency measurement of the signal for one of J segmentswithin an N sample, each J segment composed of K samples; computing aphase measurement of each J segment using the frequency computed for oneof the J segments; combining the phase measurement of each J segment togenerate a combined phase measurement indicative of the phasemeasurement of the N sample of the signal.
 11. The method as set forthin claim 10, wherein the number of K samples is determined based uponthe signal to noise ratio (SNR) of the signal.
 12. The method as setforth in claim 10, wherein the step of computing the frequency comprisesthe steps of:dividing the J segment of the signal into a plurality ofsampled signals, each sampled signal sampled at a different samplingfrequency:performing a discrete Fourier transform (DFT) on each sampledsignal; and combining the results of the DFT sampled signals todetermine the frequency.
 13. The method as set forth in claim 10,wherein the step of computing the frequency comprises using zerocrossing counting.
 14. The method as set forth in claim 10, wherein thestep of computing the frequency comprises using a fast Fourier transform(FFT).
 15. The method as set forth in claim 10, wherein the step ofcomputing a phase measurement for each J segment comprises determiningthe phase measurement according to the following:If q_(i) =1 then φ_(i)=θ If q_(i) =2 then φ_(i) =π-θ If q_(i) =3 then φ_(i) =π+θ If q_(i) =4then φ_(i) =2π-θwhere q_(i) represents the quadrant of the phasemeasurement, and θ is determined according to the following: ##EQU17##where k_(s) is the estimated signal frequency normalized to the samplingfrequency and 0≦θ<π/2.
 16. The method as set forth in claim 10, whereinthe step of combining the phase measurement of each J segment togenerate a combined phase measurement comprises the steps of:summing thephase measurement values of the J segments to generate a summed valueΦ_(ACC) ; determining the number of phase measurements that fall intoeach quadrant; and determining the combined phase measurement accordingto the following; ##EQU18## where JVAL represents the number of validphase measurements, q₁, q₂, . . . q_(JVAL) represent the quadrants ofvalid phase measurements, and q 4! represents the number of valid phasemeasurements that falls into the fourth quadrant.
 17. A circuit formeasuring phase for N samples of a signal comprising:at least onesampling circuit for sampling the signal; a frequency measurement unitcoupled to the at least one sampling circuit that computes a frequencymeasurement for one of J segments within an N sample, wherein each Jsegment is composed of K samples; and a phase measurement unit coupledto the at least one sampling circuit and the frequency measurement unitto compute a phase measurement of each J segment using the frequencycomputed for one of the J segments and to combine the phase measurementof each J segment to generate a combined phase measurement indicative ofthe phase measurement of the N sample of the signal.
 18. The circuit asset forth in claim 17, further comprising a burst detector coupled tothe output of the at least one sampling circuit and to the frequencymeasurement unit and phase measurement unit, said burst detectordetecting the presence of the signal and enables the operation of thefrequency measurement unit and phase measurement unit.
 19. The circuitas set forth in claim 17, wherein the frequency measurement unitmeasures the frequency by dividing the J segment of the signal into aplurality of sampled signals, each sampled signal sampled at a differentsampling frequency, performing a discrete Fourier transform (DFT) oneach sampled signal, and combining the results of the DFT sampledsignals to determine the frequency.
 20. The circuit as set forth inclaim 17, wherein the frequency measurement unit comprises a zerocrossing counting circuit.
 21. The circuit as set forth in claim 17,wherein the frequency measurement unit measures the frequency by using afast Fourier transform (FFT).
 22. The circuit as set forth in claim 17,wherein the phase measurement unit comprises:circuitry to compute aphase measurement for each J segment according to the following: Ifq_(i) =1 then φ_(i) =θ If q_(i) =2 then φ_(i) =π-θ If q_(i) =3 thenφ_(i) =π+θ If q_(i) =4 then φ_(i) =2π-θwhere q_(i) represents thequadrant of the phase measurement, and θ is determined according to thefollowing: ##EQU19## where k_(s) is the estimated signal frequencynormalized to the sampling frequency and 0≦θ<π/2.
 23. The circuit as setforth in claim 17, wherein the phase measurement unitcomprises:circuitry to combine the phase measurement of each J segmentto generate the combined phase measurement according to the following:an adder circuit to add the phase measurement values of the J segmentsto generate a summed value Φ_(ACC) ; logic for determining the number ofphase measurements that fall into each quadrant; and logic fordetermining the combined phase measurement according to the following;##EQU20## where JVAL represents the number of valid phase measurements,q₁, q₂, . . . q_(JVAL) represent the quadrants of valid phasemeasurements, and q 4! represents the number of valid phase measurementsthat falls into the fourth quadrant.
 24. A circuit for measuring phaseof N samples of a signal comprising the steps of:at least one lowresolution analog to digital converter (ADC) for sampling the signal; afirst logic computing a frequency measurement for one J segment of thesampled signal within an N sample, each J segment being composed of Ksamples; a second logic for computing a phase measurement of each Jsegment using stored precomputed values; and a third logic for combiningthe phase measurements of each J segment to generate the phasemeasurement for N samples.
 25. The circuit as set forth in claim 24,wherein the signal is sampled using 1-bit ADC.
 26. The circuit as setforth in claim 24, wherein the frequency is measured using the DiscreteFourier Transform (DFT).
 27. The circuit as set forth in claim 24,further comprising memory and at least one latch, wherein the sampledsignal is temporarily stored in memory and then latched by that at leastone latch.
 28. The circuit as set forth in claim 24, further comprisinglook-up tables (LUTs) used to store the precomputed values of severalsamples of the input signal with the correspondent values of thereference signal.
 29. The circuit as set forth in claim 28, wherein theinput to the LUTs are the sampled signal stored in the latches, thefrequency and the phase of the reference signal.
 30. The circuit as setforth in claim 28, wherein accumulators are used to sum the LUT'soutputs to produce values of x and y where, ##EQU21## where r(i) andq(i) represent sampled data, k_(s) represents an estimated signalfrequency normalized to the sampling frequency, and K represents thenumber of samples within a segment.
 31. The circuit as set forth inclaim 30, wherein the second logic computes the phase φ_(j) of a segmentj by computing tan⁻¹ (x/y) and the quadrant of the phase measurement.32. The circuit as set forth in claim 31, wherein the third logiccomputes the phase measurement of N samples by combining the phasemeasurements φ_(j) 's of valid segments.
 33. A circuit for measuringphase over a large amplitude dynamic range comprising:a plurality ofsampling circuits for sampling the signal, each sampling circuitsampling different segments, each segment sampled at a samplingfrequency fs; a frequency measurement unit coupled to one samplingcircuit of the plurality of sampling circuits; a phase measurement unitto measure the phase of each segment and to combine the phasemeasurements to generate a phase measurement.
 34. The circuit as setforth in claim 33, wherein at least one sampling circuit of theplurality of sampling circuits comprises a one bit analog to digitalconverter (ADC).
 35. The circuit as set forth in claim 33, wherein eachsampling circuit samples the signal for a segment using the samplingfrequency of a previous segment delayed by τ, where τ is a time delay.36. The circuit as set forth in claim 33, wherein a pattern of thesampled data at fs/4, where s represents the sampling frequency, foreach segment is different than that of other segments sampled.
 37. Thecircuit as set forth in claim 33, wherein the sampling frequency foreach segment is phase modulated.
 38. The circuit as set forth in claim33, wherein the frequency of one segment is computed using Fourieranalysis.
 39. The circuit as set forth in claim 33, wherein the phase ofeach segment is computed using Fourier analysis method.
 40. The circuitas set forth in claim 33, wherein the phase measurement of N samples ofthe input signal are computed by combining the phase measurements ofvalid segments of N samples.